In this paper we survey some notions of generalized derivative for C1,1 functions.Furthermore some optimality conditions and numerical methods for nonlinear minimization problems involving C1,1 data are studied.

In this paper some second order necessary and sucient conditions aregiven for unconstrained and constrained optimization problems involving C1functions. A generalized derivative is obtained by approximation with smoothfunctions and it collapses to Clarke's definition when C(1,1) data are...

Many definitions of second order generalized derivatives have been introduced to obtain optimality conditions for optimization problems involving C(1,1) data. The aim of this paper is to show some relations among these definitions and to study necessary and sufficient optimality conditions for...

In this work we provide a characterization of C{k,1} functions on Rn (that is k times differentiable with locally Lipschitzian k-th derivatives) by means of (k+1)-th divided differences and Riemann derivatives. In particular we prove that the class of C{k,1} functions is equivalent to the class...

In this paper some new contractive operators on C([a, b]) of IFS type arebuilt. Inverse problems are introduced and studied by convex optimizationproblems. A stability result and some optimality conditions are given.

The class of strongly semicontinuous functions is considered. For these functionsthe notion of mollified derivatives, introduced by Ermoliev, Norkin andWets [8], is extended to the second order. By means of a generalized Taylor'sformula, second order necessary and sufficient conditions are...

In this paper second-order optimality conditions for nonsmooth vector optimization problems are given by smooth approximations. We extend to the vector case the approach introduced by Ermoliev,Norkin and Wets to define generalized derivatives for discontinuous functions as limit of the classical...